Long-range Spatial Order Research Articles

PVDF/fluorescent carbon dots electrospun nanofibers with synergistic dipole alignment and multifunctional sensing applications

The development of novel multifunctional materials has been attracting continuous attention in recent years. In this work, fluorescent carbon dots (CDs) with a designed quasi-molecular structure were introduced into polyvinylidene fluoride (PVDF) nanofibers to realize electro-mechano-photoluminescence coupling effects. The N-H and O-H groups in the CDs formed hydrogen bonds with C-F groups in PVDF, which not only ensured the uniform arrangement of the CDs in the nanofiber matrix, but also facilitated the polarization of the PVDF. The β phase in PVDF was improved from 80% to 86% by doping of the CDs. Moreover, due to the asymmetric molecular structure of the carbon dot, it possessed an intrinsic dipole moment of 4.62 Debye. The self-assembly of the CDs on the nanofibers with a similar energy-favorable conformation improved the long-range spatial ordering in the nanocomposite. The CDs could also act as working dipoles, and contributed to the piezoelectric output of the whole device. Under a repeated finger imparting, the output voltage was enhanced from 6 V of the pure PVDF to 15 V of the nanocomposite. Furthermore, the CDs endowed the fiber with fluorescence capacity. The composite nanofiber exhibited bright fluorescence with excellent homogeneity. Through monitoring of the fluorescent intensity, visualized strain sensing and information encryption could be realized, which showed high potential of the nanofiber as a multifunctional nanocomposite.

Assembling Molecular Clips To Build π-Stacks.

Nature utilizes an intimate stacking of aromatic motifs to construct functional structures, as demonstrated in protein folding and polynucleotide assembly. However, organized π-stacks of artificial molecules are difficult to build, primarily due to the weak, non-directional, and context-sensitive nature of van der Waals forces. To overcome these challenges, chemists have invented ingenious architectural designs to construct π-stacked supramolecular assemblies using clip-like molecules. This Concept article focuses on molecular clips that enable precise spatial control over assembly patterns, beyond the scope of simple host-guest chemistry. Different design strategies are analyzed and compared that leverage non-covalent interactions to create multi-layer π-stacks. Particular emphasis is placed on the choice of spine units as they play a crucial role in controlling the (i) spacing, (ii) orientation, and (iii) conformational pre-organization of linked aromatics to achieve long-range spatial ordering.

Critical properties of the prethermal Floquet time crystal

The critical properties characterizing the formation of the Floquet time crystal in the prethermal phase are investigated analytically in the periodically driven $O(N)$ model. In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and absence of long-range spatial order from the non-trivial phase where long-range spatial order is accompanied by period-doubling dynamics. In the vicinity of the critical line, with a combination of dimensional expansion and exact solution for $N\to\infty$, we determine the exponent $\nu$ that characterizes the divergence of the spatial correlation length of the equal-time correlation functions, the exponent $\beta$ characterizing the growth of the amplitude of the order-parameter, as well as the initial-slip exponent $\theta$ of the aging dynamics when a quench is performed from deep in the trivial phase to the critical line. The exponents $\nu, \beta, \theta$ are found to be identical to those in the absence of the drive. In addition, the functional form of the aging is found to depend on whether the system is probed at times that are small or large compared to the drive period. The spatial structure of the two-point correlation functions, obtained as a linear response to a perturbing potential in the vicinity of the critical line, is found to show algebraic decays that are longer ranged than in the absence of a drive, and besides being period-doubled, are also found to oscillate in space at the wave-vector $\omega/(2 v)$, $v$ being the velocity of the quasiparticles, and $\omega$ being the drive frequency.

Bacterial and archaeal cytoskeletons

All living cells depend on the intricate organization of molecular components in space and time. Although this notion was historically based on eukaryotic cells, with their structured intracellular architecture and cellular morphologies, it is now recognized that prokaryotes (that is, bacteria and archaea) also possess complex structures. A cytoskeleton is a network of intracellular protein filaments that play a structural or mechanical role (such as scaffolding, pushing, or pulling) in the spatiotemporal organization of cellular processes. Polymerization of protein monomers in a roughly linear fashion into filaments represents an effective means to establish long-range spatial order by bridging the gap between nanometer-sized molecules and micron-sized cells. It is now evident that bacteria and archaea possess numerous kinds of cytoskeletal proteins, including prokaryotic homologues of the eukaryotic actins, tubulins, and intermediate filaments, as well as other types that have been found primarily or exclusively in prokaryotes (Table 1). Understanding the diverse functions and mechanisms of the rapidly growing universe of prokaryotic cytoskeletal proteins will not only advance prokaryotic cell biology and reveal evolutionary principles, but also open up new avenues for the development of anti-microbial agents, de novo protein design, and the construction of minimal and synthetic cells.

Evaporative cooling to a Rydberg crystal close to its ground state

We theoretically show how to obtain a long one-dimensional crystal near its quantum ground state. We rely on an evaporative cooling scheme applicable to many-body systems with nonzero-ranged interactions. Despite the absence of periodic potentials, the final state is a crystal which exhibits long-range spatial order. We describe the scheme thermodynamically, applying the truncated Boltzmann distribution to the collective excitations of the chain, and show that it leads to a novel quasi-equilibrium many-body state. For longer chains, comprising about 1000 atoms, we emphasize the quasi-universality of the evaporation curve. Such exceptionally long 1D crystals are only accessible deep in the quantum regime. We perform our analysis on the example of an initially thermal chain of circular Rydberg atoms confined to a one-dimensional (1D) geometry. Our scheme may be applied to other quantum systems with long-ranged interactions such as polar molecules.

Novel transition to fully absorbing state without long-range spatial order in directed percolation class

We study coupled Gauss maps in one dimension and observe a transition to band periodic state with 2 bands. This is a periodic state with period-2 in a coarse-grained sense. This state does not show any long-range order in space. We compute two different order parameters to quantify the transition a) Flipping rate F(t) which measures departures from period-2 and b) Persistence P(t) which quantifies the loss of memory of initial conditions. At the critical point, F(t) shows a power-law decay with exponent 0.158 which is close to 1-D directed percolation (DP) transition. The persistence exponent at the critical point is found to be 1.51 which matches with several models in 1-D DP class. We also study the finite-size scaling and off-critical scaling to estimate other exponents z and ν∥. We observe excellent scaling for both F(t) as well as P(t) and the exponents obtained are clearly in DP class. We believe that DP transition could be observed in systems where activity goes to zero even if the spatial profile could be inhomogeneous and lacking any long-range order.

Harnessing Medium Anisotropy To Control Active Matter.

Active matter is a wide class of nonequilibrium systems consisting of interacting self-propelled agents transducing the energy stored in the environment into mechanical motion. Numerous examples range from microscopic cytoskeletal filaments and swimming organisms (bacteria and unicellular algae), synthetic catalytic nanomotors, colloidal self-propelled Janus particles, to macroscopic bird flocks, fish schools, and even human crowds. Active matter demonstrates a remarkable tendency toward self-organization and development of collective states with the long-range spatial order. Furthermore, active materials exhibit properties that are not present in traditional materials like plastics or ceramics: self-repair, shape change, and adaptation. A suspension of microscopic swimmers, such as motile bacteria or self-propelled colloids (active suspensions), is possibly the simplest and the most explored realization of active matter. Recent studies of active suspensions revealed a wealth of unexpected behaviors, from a dramatic reduction of the effective viscosity, enhanced mixing and self-diffusion, rectification of chaotic motion, to artificial rheotaxis (drift against the imposed flow) and cross-stream migration. To date, most of the studies of active matter are performed in isotropic suspending medium, like water with the addition of some "fuel", e.g., nutrient for bacteria or H2O2 for catalytic bimetallic AuPt nanorods. A highly structured anisotropic suspending medium represented by lyotropic liquid crystal (water-soluble) opens enormous opportunities to control and manipulate active matter. Liquid crystals exhibit properties intermediate between solid and liquids; they may flow like a liquid but respond to deformations as a solid due to a crystal-like orientation of molecules. Liquid crystals doped by a small amount of active component represent a new class of composite materials (living liquid crystals or LLCs) with unusual mechanical and optical properties. LLCs demonstrate a variety of highly organized dynamic collective states, spontaneous formation of dynamic textures of topological defects (singularities of local molecular orientation), controlled and reconfigurable transport of cargo particles, manipulation of individual trajectories of microswimmers, and many others. Besides insights into fundamental mechanisms governing active materials, living liquid crystals may have intriguing applications, such as the design of new classes of soft adaptive bioinspired materials capable to respond to physical and chemical stimuli, such as light, magnetic, and electric fields, mechanical shear, airborne pollutants, and bacterial toxins. This Account details the most recent developments in the field of LLCs and discusses how the anisotropy of liquid crystals can be harnessed to control and manipulate active materials.

Prediction of a Mobile Solid State in Dense Hydrogen under High Pressures.

Solid rigidity and liquid-scale mobility are thought to be incompatible in elemental substances. One cannot have an elemental solid that is long-range positionally ordered wherein the atoms flow like in a liquid simultaneously. The only exception might be the hypothetical supersolid state of 4He. In this work, we demonstrate that such exotic state could exist even in the classical regime. Using ab initio molecular dynamics (AIMD) and ab initio path integral molecular dynamics (AI-PIMD), a novel state of dense hydrogen that simultaneously has both long-range spatial ordering and liquid-scale atomic mobility is discovered at 1 to 1.5 TPa (1 TPa ≈ 10 000 000 atmospheric pressures). The features distinct from a normal solid and liquid are carefully characterized, and the stability and melting behavior are investigated. Extensive AI-PIMD simulations further revealed that this state might be (meta-)stable even at ultralow temperatures, suggesting an emerging candidate for an alternative type of supersolid state in dense metallic hydrogen.

Residual Defect Density in Random Disks Deposits.

We investigate the residual distribution of structural defects in very tall packings of disks deposited randomly in large channels. By performing simulations involving the sedimentation of up to 50 × 109 particles we find all deposits to consistently show a non-zero residual density of defects obeying a characteristic power-law as a function of the channel width. This remarkable finding corrects the widespread belief that the density of defects should vanish algebraically with growing height. A non-zero residual density of defects implies a type of long-range spatial order in the packing, as opposed to only local ordering. In addition, we find deposits of particles to involve considerably less randomness than generally presumed.

Self-organization in cold atomic gases: a synchronization perspective.

We study non-equilibrium spatial self-organization in cold atomic gases, where long-range spatial order spontaneously emerges from fluctuations in the plane transverse to the propagation axis of a single optical beam. The self-organization process can be interpreted as a synchronization transition in a fully connected network of fictitious oscillators, and described in terms of the Kuramoto model.

Shape-induced chiral ordering in two-dimensional packing of snowmanlike dimeric particles

Understanding the distinctive phase behaviors in random packing due to particle shapes is an important issue in condensed matter physics. In this paper, we investigate the random packing structure of two-dimensional (2D) snowmen via wax-snowman packing experiments and Brownian dynamics simulations. Both experiments and simulations reveal that neighboring snowmen have a strong short-range orientational correlation and consequently locally form particular conformations. A chiral conformation is dominant for high area fractions near the jamming condition (φ>0.8), and the proportion of the chiral conformation increases with γ. We also found that the attractive interaction does not have a significant impact on the results. The geometry of chirally ordered snowmen causes a mismatch with 2D crystalline symmetries and thus inhibits the development of long-range spatial order, despite the strong orientational correlation between neighbors.

Three distinct types of quantum phase transitions in a (2+1)-dimensional array of dissipative Josephson junctions

We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range spatial ordering in the phase $\theta$ of the superconducting order parameter, but temporal ordering only in spatial gradients $\Delta \theta$, not in $\theta$. Significantly, the most ordered state therefore does not have 3D XY ordering. Rather, it features 2D spin waves coexisting with temporally disordered phases $\theta$. There is also an intermediate phase featuring quasi-long-range spatial order in $\theta$ coexisting with a gas of instantons in $\Delta \theta$. We briefly discuss possible experimental signatures of such a state, which may be viewed as a local metal and a global superconductor. The most disordered state has phase disorder in all spatio-temporal directions, and may be characterized as a gas of proliferated vortices coexisting with a gas of $\Delta \theta$-instantons. The phase transitions between these phases are discussed. The transition from the most ordered state to the intermediate state is driven by proliferation of instantons in $\Delta \theta$. The transition from the intermediate state to the most disordered state is driven by the proliferation of spatial point vortices in the background of a proliferated $\Delta \theta$-instanton gas, and constitutes a Berezinskii-Kosterlitz-Thouless phase transition. The model also features a direct phase transition from the most ordered state to the most disordered state, and this transition is neither in the 2D XY nor in the 3D XY universality class. It comes about via a simultaneous proliferation of point vortices in two spatial dimensions and $\Delta \theta$-instantons, with a complicated interplay between them.

Two‐Dimensional Self‐Organization of an Ordered Au Silicide Nanowire Network on a Si(110)‐16 × 2 Surface

A well-ordered two-dimensional (2D) network consisting of two crossed Au silicide nanowire (NW) arrays is self-organized on a Si(110)-16 x 2 surface by the direct-current heating of approximately 1.5 monolayers of Au on the surface at 1100 K. Such a highly regular crossbar nanomesh exhibits both a perfect long-range spatial order and a high integration density over a mesoscopic area, and these two self-ordering crossed arrays of parallel-aligned NWs have distinctly different sizes and conductivities. NWs are fabricated with widths and pitches as small as approximately 2 and approximately 5 nm, respectively. The difference in the conductivities of two crossed-NW arrays opens up the possibility for their utilization in nanodevices of crossbar architecture. Scanning tunneling microscopy/spectroscopy studies show that the 2D self-organization of this perfect Au silicide nanomesh can be achieved through two different directional electromigrations of Au silicide NWs along different orientations of two nonorthogonal 16 x 2 domains, which are driven by the electrical field of direct-current heating. Prospects for this Au silicide nanomesh are also discussed.

Ultrafast microfluidics using surface acoustic waves.

We demonstrate that surface acoustic waves (SAWs), nanometer amplitude Rayleigh waves driven at megahertz order frequencies propagating on the surface of a piezoelectric substrate, offer a powerful method for driving a host of extremely fast microfluidic actuation and microbioparticle manipulation schemes. We show that sessile drops can be translated rapidly on planar substrates or fluid can be pumped through microchannels at 1-10 cms velocities, which are typically one to two orders quicker than that afforded by current microfluidic technologies. Through symmetry-breaking, azimuthal recirculation can be induced within the drop to drive strong inertial microcentrifugation for micromixing and particle concentration or separation. Similar micromixing strategies can be induced in the same microchannel in which fluid is pumped with the SAW by merely changing the SAW frequency to rapidly switch the uniform through-flow into a chaotic oscillatory flow by exploiting superpositioning of the irradiated sound waves from the sidewalls of the microchannel. If the flow is sufficiently quiescent, the nodes of the transverse standing wave that arises across the microchannel also allow for particle aggregation, and hence, sorting on nodal lines. In addition, the SAW also facilitates other microfluidic capabilities. For example, capillary waves excited at the free surface of a sessile drop by the SAW underneath it can be exploited for micronanoparticle collection and sorting at nodal points or lines at low powers. At higher powers, the large accelerations off the substrate surface as the SAW propagates across drives rapid destabilization of the drop free surface giving rise to inertial liquid jets that persist over 1-2 cm in length or atomization of the entire drop to produce 1-10 mum monodispersed aerosol droplets, which can be exploited for ink-jet printing, mass spectrometry interfacing, or pulmonary drug delivery. The atomization of polymerprotein solutions can also be used for the rapid synthesis of 150-200 nm polymerprotein particles or biodegradable polymeric shells in which proteins, peptides, and other therapeutic molecules are encapsulated within for controlled release drug delivery. The atomization of thin films behind a translating drop containing polymer solutions also gives rise to long-range spatial ordering of regular polymer spots whose size and spacing are dependent on the SAW frequency, thus offering a simple and powerful method for polymer patterning without requiring surface treatment or physicalchemical templating.

Spatial ordering and anisotropy in surface stress domains and nanostructural evolution

The role of elastic interaction has been well recognized for various growth modes and nanostructural self-organization on solid surfaces. Examples include spontaneous formation of stress domains in reconstructed surfaces or in-phase-separating monolayers, meandering and bunching of surface steps, and quantum dot formation in heteroepitaxial thin film growth. The long-range spatial ordering in these strain-mediated nanostructural evolution phenomena on solid surfaces is critically dependent on the anisotropy. A universal formulation has been developed to examine the energetically favored orientation with respect to parameters that represent the anisotropy in elasticity and applied stress.

Long-range ordered nanoaperture array with uniform diameter and interpore spacing

In application of focused-ion-beam lithography and grazing Ar+ milling on the U-shape barrier layer of anodic alumina nanochannels, we fabricated a hexagonally symmetry aperture array with nominal diameter of 12±2nm and interspacing of 100±2nm. Besides long-range spatial ordering, the focused-ion-beam guided-grown process has also significantly improved uniformity of both the interpore spacing and the aperture size. This aperture array membrane can be applied to the fabrication of nanostructures, such as a lithographic contact mask for ordered quantum-dot array.

Atom Interferometric Detection of the Pairing Order Parameter in a Fermi Gas

We propose two interferometric schemes to experimentally detect in real space the onset of pair condensation in a two-spin-component Fermi gas. Two atomic wave packets are coherently extracted from the gas at different positions and are mixed by a matter-wave beam splitter: we show that the spatial long-range order of the atomic pairs in the gas reflects in the atom counting statistics in the beam splitter output channels. The same long-range order is also shown to create a matter-wave grating in the overlapping region of the two extracted wave packets, grating that can be revealed by a light-scattering experiment.

Plasmon-waveguide Resonance Studies of Lateral Segregation of Lipids and Proteins into Microdomains (Rafts) in Solid-supported Bilayers

Plasmon-waveguide resonance (PWR) spectroscopy has been used to examine solid-supported lipid bilayers consisting of dioleoylphosphatidylcholine (DOPC), palmitoyloleoylphosphatidylcholine (POPC), sphingomyelin (SM), and phosphatidylcholine/SM binary mixtures. Spectral simulation of the resonance curves demonstrated an increase in bilayer thickness, long-range order, and molecular packing density in going from DOPC to POPC to SM single component bilayers, as expected based on the decreasing level of unsaturation in the fatty acyl chains. DOPC/SM and POPC/SM binary mixtures yielded PWR spectra that can be ascribed to a superposition of two resonances corresponding to microdomains (rafts) consisting of phosphatidylcholine- and SM-rich phases coexisting within a single bilayer. These were formed spontaneously over time as a consequence of lateral phase separation. Each microdomain contained a small proportion (<20%) of the other lipid component, which increased their kinetic and thermodynamic stability. Incorporation of a glycosylphosphatidylinositol-linked protein (placental alkaline phosphatase) occurred within each of the single component bilayers, although the insertion was less efficient into the DOPC bilayer. Incorporation of placental alkaline phosphatase into a DOPC/SM binary bilayer occurred with preferential insertion into the SM-rich phase, although the protein incorporated into both phases at higher concentrations. These results demonstrate the utility of PWR spectroscopy to provide insights into raft formation and protein sorting in model lipid membranes.

Submicrometer spatial resolution of metal-enhanced fluorescence.

Enhanced fluorescence emission intensity from fluorescein was observed on glass slides covered with thin films of silver nanoparticles using a confocal laser-scanning microscope. The silver nanoparticle film increased the emission intensity of fluorescein by an average of at least three-fold in the area studied. Statistics are given on the enhancement of individual areas of the silver particle film with a resolution of approximately 210 nm. A histogram of intensity values indicates that the enhancement appears to occur without distinct subpopulations, with the exception that very high intensity subpopulations may occur but could not be resolved. Spatial features with dimensions near or smaller than the resolution limit of the confocal microscope, on the silver nanoparticle slide that enhanced the emission of fluorescein, were found using autocorrelation functions. These spatial features are of the same size as those found from the emission of slides containing silver nanoparticles only. These spatial features do not appear in control slides containing fluorescein without any silver nanoparticles. No long-range spatial ordering of the fluorescence enhancement on chemcially deposited silver nanoparticle slides was detected.

Photonic Materials from Self-Assembly of “Tolerant” Core−Shell Coated Colloids

The self-assembly of core−shell colloids into ordered arrays holds promise as a convenient method for the fabrication of photonic opals or as templates for inverse opaline materials. Recent advances in the layer-by-layer (LbL) technique for coating colloids have made it possible to create composite core−shell materials with exquisite control over the thickness and chemical composition of the shell. Here, we demonstrate that modification of the outer surface of the LbL-coated colloids by grafting a brush layer (comprising a water-soluble poly(ethylene oxide) copolymer) renders them highly “tolerant” to the formation of ordered opals. Ordered assemblies with long-range spatial order are readily formed by drying such surface-modified coated colloids in a flow cell that we have specially designed to construct films with a defined thickness. We demonstrate the assembly of films from brush-modified polyelectrolyte-coated colloids and their characterization using electron microscopy and transmission optical spec...